-
2
-
-
0001578518
-
A learning algorithm for Boltzmann machines
-
D. H. Ackley, G. E. Hinton, and T. J. Sejnowski, “A learning algorithm for Boltzmann machines,” Cognitive Science, vol. 9, pp. 147–169, 1985.
-
(1985)
Cognitive Science
, vol.9
, pp. 147-169
-
-
Ackley, D.H.1
Hinton, G.E.2
Sejnowski, T.J.3
-
4
-
-
0000344740
-
Differential geometry of curved exponential families—Curvatures and information loss
-
S. Amari, “Differential geometry of curved exponential families—Curvatures and information loss,” Annals of Statistics, vol. 10, no. 2, pp. 357–385, 1982.
-
(1982)
Annals of Statistics
, vol.10
, Issue.2
, pp. 357-385
-
-
Amari, S.1
-
5
-
-
0003355631
-
Differential-Geometrical Methods in Statistics &lpar
-
’. New York: Springer
-
S. Amari, Differential-Geometrical Methods in Statistics ‘ Springer Lecture Notes in Statistics vol. 28’. New York: Springer, 1985.
-
(1985)
Springer Lecture Notes in Statistics
, vol.28
-
-
Amari, S.1
-
6
-
-
4243592137
-
Differential geometry of smooth families of probability distributions
-
METR 82-7, Univ. Tokyo
-
H. Nagaoka and S. Amari, “Differential geometry of smooth families of probability distributions,” METR 82-7, Univ. Tokyo, 1982.
-
(1982)
-
-
Nagaoka, H.1
Amari, S.2
-
7
-
-
84941538115
-
-
Differential Geometry in Statistical Inferences ‘IMS Lecture Notes Monograph Series, ’. IMS CA: Hayward
-
S. Amari, O. E. Barndorff-Hielsen, R. E. Kass, S. L. Lauritzen, and C. R. Rao, Differential Geometry in Statistical Inferences ‘IMS Lecture Notes Monograph Series, vol. 10’. IMS CA: Hayward, 1987.
-
(1987)
, vol.10
-
-
Amari, S.1
Barndorff-Hielsen, O.E.2
Kass, R.E.3
Lauritzen, S.L.4
Rao, C.R.5
-
9
-
-
0000143473
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Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference
-
M. Kumon and S. Amari, “Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference,” in Proc. R. Soc. London, A387, pp. 429–458, 1983.
-
(1983)
Proc. R. Soc. London
, vol.A387
, pp. 429-458
-
-
Kumon, M.1
Amari, S.2
-
10
-
-
0000460064
-
Estimation in the presence of infinitely many nuisance parameters—Geometry of estimating functions
-
S. Amari and M. Kumon, “Estimation in the presence of infinitely many nuisance parameters—Geometry of estimating functions,” Annals of Statistics, vol. 16, pp. 1044–1068, 1988.
-
(1988)
Annals of Statistics
, vol.16
, pp. 1044-1068
-
-
Amari, S.1
Kumon, M.2
-
11
-
-
0010935923
-
Asymptotic theory of sequential estimation: Differential geometrical approach
-
I. Okamoto, S. Amari and K. Takeuchi, “Asymptotic theory of sequential estimation: Differential geometrical approach,” Annals of Statistics, vol. 19, pp. 961–981, 1991.
-
(1991)
Annals of Statistics
, vol.19
, pp. 961-981
-
-
Okamoto, I.1
Amari, S.2
Takeuchi, K.3
-
12
-
-
0002975366
-
Differential geometry of a parametric family of invertible linear systems—Riemannian metric, dual affine connections and divergence
-
S. Amari “Differential geometry of a parametric family of invertible linear systems—Riemannian metric, dual affine connections and divergence,” Mathematical Systems Theory, vol. 20, pp. 53-82, 1987.
-
(1987)
Mathematical Systems Theory
, vol.20
, pp. 53-82
-
-
Amari, S.1
-
13
-
-
0024629649
-
Statistical inference under multiterminal rate restrictions—A differential geometrical approach
-
S. Amari and T. S. Han, “Statistical inference under multiterminal rate restrictions—A differential geometrical approach,” IEEE Trans. Inform. Theory, vol. IT-35, pp. 217–227, 1989.
-
(1989)
IEEE Trans. Inform. Theory
, vol.IT-35
, pp. 217-227
-
-
Amari, S.1
Han, T.S.2
-
14
-
-
33747470032
-
Fisher information under restriction of Shannon information in multiterminal situations
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S. Amari, “Fisher information under restriction of Shannon information in multiterminal situations,” Ann. Inst. Statist. Math. 41, no. 4, pp. 623–648, 1989.
-
(1989)
Ann. Inst. Statist. Math. 41
, Issue.4
, pp. 623-648
-
-
Amari, S.1
-
15
-
-
0021518209
-
Stochastic relaxation, Gibbs distribution, and the Bayestan restoration of images
-
S. Geman and D. Geman, “Stochastic relaxation, Gibbs distribution, and the Bayestan restoration of images,” IEEE Trans., Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721–741, 1984.
-
(1984)
IEEE Trans., Pattern Anal. Machine Intell.
, vol.PAMI-6
, pp. 721-741
-
-
Geman, S.1
Geman, D.2
-
17
-
-
0025508916
-
A statistical approach to learning and generalization in layered neural networks
-
E. Levin, N. Tishby and S. A. Solla, “A statistical approach to learning and generalization in layered neural networks,” Proc. IEEE, vol. 78, pp. 1568–1574, 1990.
-
(1990)
Proc. IEEE
, vol.78
, pp. 1568-1574
-
-
Levin, E.1
Tishby, N.2
Solla, S.A.3
-
18
-
-
84956887606
-
Statistical mechanics of learning from examples
-
to appear.
-
H. Seung and H. E. Sompolinski, “Statistical mechanics of learning from examples,” Phys. Rev. A, to appear.
-
Phys. Rev. A
-
-
Seung, H.1
Sompolinski, H.E.2
-
19
-
-
0025488578
-
Mathematical foundations of neurocomputing
-
S. Amari, “Mathematical foundations of neurocomputing,” Proc. IEEE, vol. 78, pp. 1443–1463, 1990.
-
(1990)
Proc. IEEE
, vol.78
, pp. 1443-1463
-
-
Amari, S.1
-
20
-
-
0025898312
-
Dualistic geometry of the manifold of higher-order neurons
-
S. Amari, “Dualistic geometry of the manifold of higher-order neurons,” Neural Networks, vol. 4, pp. 443–451, 1991.
-
(1991)
Neural Networks
, vol.4
, pp. 443-451
-
-
Amari, S.1
-
21
-
-
0001915002
-
Information and accuracy attainable in the estimation of statistical parameters
-
C. R. Rao, “Information and accuracy attainable in the estimation of statistical parameters,” Bull. Calcutta Math. Soc., vol. 37, pp. 81–91, 1945.
-
(1945)
Bull. Calcutta Math. Soc.
, vol.37
, pp. 81-91
-
-
Rao, C.R.1
-
22
-
-
0002303010
-
The role of differential geometry in statistical theory
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O. Barndorf-Nielsen, D. R. Cox, and N. Reid, “The role of differential geometry in statistical theory,” Int. Statist. Rev., vol. 54, pp. 83–96, 1986.
-
(1986)
Int. Statist. Rev.
, vol.54
, pp. 83-96
-
-
Barndorf-Nielsen, O.1
Cox, D.R.2
Reid, N.3
-
23
-
-
84972503977
-
The geometry of asymptotic inference
-
R. E. Kass, “The geometry of asymptotic inference,” Statistical Science, vol. 4, pp. 188–234, 1989.
-
(1989)
Statistical Science
, vol.4
, pp. 188-234
-
-
Kass, R.E.1
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